Method for determining the axial position of formation layer boundaries using measurements made by a transverse electromagnetic induction logging instrument

ABSTRACT

A method for estimating axial positions of formation layer boundaries from transverse electromagnetic induction signals. A first derivative is calculated with respect to depth of the induction signals. A second derivative of the signals is calculated. The second derivative is muted. Layer boundaries are selected at axial positions where the muted second derivative is non zero, and the first derivative changes sign. The selected boundaries are thickness filtered to eliminate boundaries which have the same axial spacing as the spacing between an induction transmitter and receiver used to measure the induction signals, and to eliminate boundaries having a spacing less than an axial resolution of the induction signals. In a preferred embodiment, the process is repeated using transverse induction measurements made at another alternating current frequency. Layer boundaries selected in both frequencies are determined to be the layer boundaries. An alternative embodiment includes Fourier transforming the induction signals into the spatial frequency domain, low pass filtering the Fourier transformed signals at a band limit about equal to the axial resolution of the induction signals, calculating a central first derivative of the filtered, Fourier transformed signals, calculating an inverse Fourier transform of the central first derivative, determining roots of the inverse Fourier transform, and testing localized properties of the inverse Fourier transform within a selected number of data sample points of the selected roots, thereby providing indications of formation layer boundaries at axial positions most likely to be true ones of the formation layer boundaries.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of application Ser. No.08/686,848 filed on Jul. 26, 1996, entitled, "Method and Apparatus forTransverse Electromagnetic Induction Logging", and assigned to theassignee of this invention, now U.S. Pat. No. 5,781,436.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention is related to the field of electromagnetic induction welllogging for determining the electrical resistivity of earth formationspenetrated by a wellbore. More specifically, the invention is related tomethods for processing induction voltage measurements to determine theposition of formation layer boundaries for inversion processing.

2. Description of the Related Art

Electromagnetic induction resistivity well logging instruments are wellknown in the art. Electromagnetic induction resistivity well logginginstruments are used to determine the electrical conductivity (and itsconverse, resistivity) of earth formations penetrated by a wellbore.Measurements of the electrical conductivity are used for, among otherthings, inferring the fluid content of the earth formations. Typically,lower conductivity (higher resistivity) is associated withhydrocarbon-bearing earth formations.

The physical principles of electromagnetic induction resistivity welllogging are described, for example, in, H. G. Doll, Introduction toInduction Logging and Application to Logging of Wells Drilled with OilBased Mud, Journal of Petroleum Technology, vol. 1, p.148, Society ofPetroleum Engineers, Richardson Tex. (1949). Many improvements andmodifications to electromagnetic induction resistivity instruments havebeen devised since publication of the Doll reference, supra. Examples ofsuch modifications and improvements can be found, for example, in U.S.Pat. No. 4,837,517, U.S. Pat. No. 5,157,605 issued to Chandler et al,and U.S. Pat. No. 5,452,762 issued to Beard et al.

A limitation to the electromagnetic induction resistivity well logginginstruments known in the art is that they typically include transmittercoils and receiver coils wound so that the magnetic moments of thesecoils are substantially parallel only to the axis of the instrument.Eddy currents are induced in the earth formations from the magneticfield generated by the transmitter coil, and in the inductioninstruments known in the art these eddy currents tend to flow in groundloops which are substantially perpendicular to the axis of theinstrument. Voltages are then induced in the receiver coils related tothe magnitude of the eddy currents. Certain earth formations, however,consist of thin layers of electrically conductive materials interleavedwith thin layers of substantially non-conductive material. The responseof the typical electromagnetic induction resistivity well logginginstrument will be largely dependent on the conductivity of theconductive layers when the layers are substantially parallel to the flowpath of the eddy currents. The substantially non-conductive layers willcontribute only a small amount to the overall response of the instrumentand therefore their presence will typically be masked by the presence ofthe conductive layers. The non-conductive layers, however, are the oneswhich are typically hydrocarbon-bearing and are of the most interest tothe instrument user. Some earth formations which might be of commercialinterest therefore may be overlooked by interpreting a well log madeusing the electromagnetic induction resistivity well logging instrumentsknown in the art.

One solution to the limitation of the induction instruments known in theart is to include a transverse transmitter coil and a transversereceiver coil on the induction instrument, whereby the magnetic momentsof these transverse coils is substantially perpendicular to the axis ofthe instrument. Such as solution was suggested in, L. A. Tabarovsky andM. I. Epov, Geometric and Frequency Focusing in Exploration ofAnisotropic Seams, Nauka, USSR Academy of Science, Siberian Division,Novosibirsk, pp. 67-129 (1972). Tabarovsky and Epov suggest variousarrangements of transverse transmitter coils and transverse receivercoils, and present simulations of the responses of these transverse coilsystems configured as shown therein. Tabarovsky and Epov also describe amethod of substantially reducing the effect on the voltage induced intransverse receiver coils which would be caused by eddy currents flowingin the wellbore. The wellbore is typically filled with a conductivefluid known as drilling mud. Eddy currents which flow in the drillingmud can substantially affect the magnitude of voltages induced in thetransverse receiver coils. The wellbore signal reduction methoddescribed by Tabarovsky and Epov can be described as "frequencyfocusing", whereby induction voltage measurements are made at more thanone frequency, and the signals induced in the transverse receiver coilsare combined in a manner so that the effects of eddy currents flowingwithin certain geometries, such as the wellbore, can be substantiallyeliminated from the final result. Tabarovsky and Epov, however, do notsuggest any configuration of signal processing circuitry which couldperform the frequency focusing method suggested in their paper.

A device which can measure "frequency focused" transverse inductionmeasurements is described in co-pending patent application Ser. No.08/686,848 filed on Jul. 26, 1996, U.S. Pat. No. 5,781,436, entitled,"Method and Apparatus for Transverse Electromagnetic Induction Logging",and assigned to the assignee of this invention. Using measurements madefrom conventional induction logging instruments such as described in U.S. Pat. No. 4,837,517, U.S. Pat. No. 5,157,605 issued to Chandler et al,and U.S. Pat. No. 5,452,762 issued to Beard et al typically involves aprocess known as inversion. Inversion includes generating an initialestimate of the probable spatial distributions of resistivity around thelogging instrument, and using the estimated spatial distribution togenerate an expected response of the particular logging instrument giventhe estimated spatial distribution of resistivity. Differences betweenthe expected response and the measured response are used to adjust themodel of spatial distribution. The adjusted model of spatialdistribution is then used to generate a new expected instrumentresponse. The new expected response is then compared to the measuredresponse. This process is repeated until the difference between theexpected response and the measured response reaches a minimum. Theapparent spatial distribution of resistivity which generates this"closest" expected response is deemed to be the distribution which mostaccurately represents the spatial distribution of resistivities in theearth formations surveyed by the induction logging instrument. See forexample U.S. Pat. No. 5,703,773 issued to Tabarovsky et al.

Inversion methods for processing signals such as from the instrumentdescribed in patent application Ser. No. 08/686,848 generally require aninitial estimate of the axial location (depth position) of theboundaries between layers of the earth formation. Initial estimates canbe made from various well log measurements such as gamma ray radiationor spontaneous potential. Gamma ray and spontaneous potential-basedmethods for determining boundary positions tend to have a relativelyhigh incidence of failure to locate boundaries or falsely indicating thepresence of a boundary where the contrast in formation resistivity isunlikely to have a material effect on the response of an inductionresistivity instrument.

SUMMARY OF THE INVENTION

The invention is a method for estimating the axial (depth) positions offormation layer boundaries from transverse electromagnetic inductionsignals measured at a selected frequency. A first derivative iscalculated with respect to depth of the transverse induction signals. Asecond derivative with respect to depth is calculated of the transverseinduction signals. The second derivative with respect to depth is mutedby "zeroing" all values falling below a predetermined threshold. Layerboundaries are selected at axial positions where the muted secondderivative is not equal to zero, and where the first derivative changessign. The selected layer boundaries are then "thickness filtered" toeliminate ones of the selected boundaries which have the same axialspacing as an axial spacing between an induction transmitter and aninduction receiver used to measure the transverse induction signals, andthe selected boundaries are filtered to eliminate ones of the selectedboundaries having an axial spacing less than an axial resolution of thetransverse electromagnetic induction signals.

In a preferred embodiment of the invention, the process of calculatingfirst and second derivatives is repeated using transverse inductionsignals measured at an alternating current frequency different from theselected frequency. Layer boundaries thus selected which appear in theprocessed induction signals measured at both frequencies are determinedto be the layer boundaries. The process can be repeated for transverseinduction measurements made at a plurality of different frequencies toimprove the reliability of the results.

An alternative embodiment of the invention includes processingtransverse electromagnetic induction signals measured at a selectedfrequency. The processing includes Fourier transforming the inductionsignals into the spatial frequency domain, low pass filtering theFourier transformed signals at a band limit about equal to an axialresolution of the induction signals, calculating a central firstderivative of the low pass filtered Fourier transformed signals,calculating an inverse Fourier transform of the central firstderivative, determining and selecting roots of the inverse Fouriertransformed central first derivative, and testing localized propertiesof the inverse Fourier transformed central first derivative within aselected number of data sample points of the selected roots, therebyproviding indications of formation layer boundaries at axial positionsmost likely to be true ones of the formation layer boundaries. Theprocess of the alternative embodiment may be repeated using transverseinduction signals measured at a different alternating current frequency.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows an induction instrument disposed in a wellbore penetratingearth formations.

FIG. 2 shows a functional block diagram of the induction instrument ofthe invention.

FIG. 3A shows the transmitter coil portion of the coil mandrel unit ofthe instrument in more detail.

FIG. 3B shows the receiver coil portion of the coil mandrel unit of theinstrument in more detail.

FIG. 4 shows a functional block diagram of a transmitter controller andsignal generator for the instrument.

FIG. 5A shows a graph of the component frequencies of the transmittercurrent.

FIG. 5B shows a graph of the composite waveform of the transmittercurrent.

FIG. 6A show a graph of the voltage induced in the receiver coil as aresult of the current shown in FIG. 5B flowing through the transmittercoil.

FIG. 6B shows the components of the voltage induced in the receiver andhow digital samples made at certain times represents the difference inpeak amplitude between the two components of the induced voltage.

FIG. 7 shows a synthesized voltage response of the X-axis receiver coilto the X-axis transmitter in a simulated earth formation havinganisotropic layers embedded in an isotropic earth formation.

FIG. 8 shows a second derivative with respect to depth of the syntheticvoltage response shown in FIG. 7.

FIG. 9 shows the second derivative curve in FIG. 8 after muting.

FIG. 10 shows the muted second derivative curve in FIG. 9 afterthickness filtering.

FIG. 11 is a flow chart of an alternative embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

1. Apparatus for measuring transverse induction signals

FIG. 1 shows an electromagnetic induction resistivity well logginginstrument 10 disposed in a wellbore 2 drilled through earth formations.The earth formations are shown generally at 4. The instrument 10 can belowered into and withdrawn from the wellbore 2 by means of an armoredelectrical cable 6 or similar conveyance known in the art. Theinstrument 10 can be assembled from three subsections: an auxiliaryelectronics unit 14 disposed at one end of the instrument 10; a coilmandrel unit 8 attached to the auxiliary electronics unit 14; and areceiver/signal processing/telemetry electronics unit 12 attached to theother end of the coil mandrel unit 8, this unit 12 typically beingattached to the cable 6.

The coil mandrel unit 8 includes induction transmitter and receivercoils, as will be further explained, for inducing electromagnetic fieldsin the earth formations 4 and for receiving voltage signals induced byeddy currents flowing in the earth formations 4 as a result of theelectromagnetic fields induced therein.

The auxiliary electronics unit 14, as will be further explained, caninclude a signal generator and power amplifiers to cause alternatingcurrents of selected frequencies to flow through transmitter coils inthe coil mandrel unit 8.

The receiver/signal processing/telemetry electronics unit 12, as will befurther explained, can include receiver circuits for detecting voltagesinduced in receiver coils in the coil mandrel unit 8, and circuits forprocessing these received voltages into signals representative of theconductivities of various layers, shown as 4A through 4F of the earthformations 4. As a matter of convenience for the system designer, thereceiver/signal processing/telemetry electronics unit 12 can includesignal telemetry to transmit the conductivity-related signals to theearth's surface along the cable 6 for further processing, oralteratively can store the conductivity related signals in anappropriate recording device (not shown) for processing after theinstrument 10 is withdrawn from the wellbore 2.

The electrical configuration of the instrument 10 can be betterunderstood by referring to a functional block diagram of the instrument10 shown in FIG. 2. The auxiliary electronics unit 14 can include atransmitter controller 24 and a combination analog to digitalconverter/digital signal processing unit (ADC/DSP) 26, both of which arepreferably enclosed in a thermal insulating flask 28. The flask 28 canbe of a type known in the art and is provided to maintain stabletemperature, and consequently stable frequency, of the transmittercontroller 24 and ADC/DSP 26. The transmitter controller 24 and ADC/DSP26 preferably receive electrical power from a DC-DC converter 30. Theelectrical power is preferably conducted along a power line 30A asdirect current, so that as the power passes through the mandrel unit 8on the way to the auxiliary electronics unit 14 the electrical powerwill not materially increase the amount of stray voltage induced incoils in the mandrel unit 8. The transmitter controller 24 can include asignal generator, which will be further explained, for generating analternating voltage signal at two different frequencies. An analogsignal output 24A of the transmitter controller 24 can be connected to atimer controller 22 which selectively operates, at an appropriate timeas will be further explained, each of three power amplifiers 16, 18, 20.The output of each of the power amplifiers 16, 18, 20 is connected toone corresponding transmitter coil set (not shown in FIG. 2) in themandrel unit 8.

The ADC/DSP 26 can be connected to a reference tap on the output of eachpower amplifier 16, 18, 20. A portion of the current flowing througheach transmitter coil (located in the mandrel unit 8) from poweramplifiers 16, 18, 20 is conducted provide a transmitter currentreference for the transmitter controller 24, and for receiver circuitslocated in the receiver/signal processing/telemetry electronics unit 12,as will be further explained. The current so detected can be digitizedin the ADC/DSP 26 to provide the transmitter current reference indigital form to the transmitter controller 24. The use of thetransmitter current reference will be further explained.

The receiver/signal processing/telemetry electronics unit 12 can includepreamplifiers 32, 34, 36, 38, 40 each of which is connected to one ofthe receiver coil sets (which will be further explained) in the coilmandrel unit 8. The output of each preamplifier can be connected to acorresponding analog-to-digital converter/digital signal processor(ADC/DSP), shown as 54, 52, 50, 48, 46 wherein the output of eachpreamplifier 32, 34, 36, 38, 40 is digitized and processed into a signalcorresponding to the voltages induced in the corresponding receiver coil(not shown in FIG. 2) to which each preamplifier is connected. Timing ofoperation for the ADC/DSP circuits 54, 52, 50, 48, 46 can be provided bya controller 56. Preferably, controller 56 operates the ADC/DSP circuits54, 52, 50, 48, 46 so that digital signal samples are made by the ADCportion of each ADC/DSP circuit at a predetermined time with respect tothe generation of the alternating current flowing through thetransmitter coils. The time can be determined by a clock andsynchronization signals conducted over control line 30B from thetransmitter controller 24. The controller 56 preferably timesdigitization from each ADC/DSP circuit so that the digital samples aresynchronized with respect to the same signal phase in each cycle of thealternating voltage induced in each receiver coil. In this manner, thesignal samples can be synchronously stacked to reduce noise in thesignal output from each ADC/DSP circuit. A method of synchronousstacking signal digital signal samples to reduce noise is described inU.S. Pat. No. 5,452,762 issued to Beard et al. The ADC/DSP circuits 54,52, 50, 48, 46 in the receiver/signal processing/telemetry electronicsunit 12 can be similar in design to the ADC/DSP 26 in the auxiliaryelectronics unit 8 as a matter of convenience for the system designer.

The receiver/signal processing/telemetry electronics unit 12 can alsoinclude a calibration circuit 42 and an associated ADC/DSP circuit 44connected thereto. A portion of the alternating current signal used todrive the power amplifiers 16, 18, 20 can be conducted to thecalibration circuit 42 over analog signal line 30C. Analog signal line30C is preferably electrostatically shielded to reduce parasiticinduction of the alternating current signal into the receiver coils inthe coil mandrel unit 8. On command from the controller 56, thecalibration circuit 42 periodically conducts a sample of the alternatingcurrent to each of the receiver preamplifiers 32, 34, 36, 38, 40. Sincethe alternating current signal thus conducted to the preamplifiers is ineach case substantially identical, small differences in responsecharacteristics of each preamplifier can be determined. The alternatingcurrent signal conducted to the preamplifiers is also digitized in aseparate ADC/DSP 44 to generate a reference signal for determining theresponse characteristics of each preamplifier. The digitized output ofeach preamplifier from ADC/DSP's 46-54 is conducted, along with thedigitized reference to the controller, where the response of eachpreamplifier can be determined as the change in the reference signalcorresponding to each preamplifier when compared to the referencesignal. Any necessary adjustments to the response of the preamplifiers46-54 may be performed numerically by adjusting the acquisition timingand numerical gain applied to digital samples from each ADC/DSP to matchthe measured difference in response between the reference signal and theoutput of each of the preamplifiers 46-54. This response calibrationsystem is provided so that the measurements of the voltages induced ineach receiver coil will be less affected by variations in response ofeach of the preamplifiers.

The controller 56 receives digital signal samples from each ADC/DSPconnected to it and calculates the magnitudes of the voltages induced ineach one of the receiver coils in the mandrel unit 8 based on the outputof the respectively interconnected ADC/DSP's 54, 52, 50, 48, 46, 44. Theinduced voltage magnitudes thus calculated in the controller 56 may beconducted to a telemetry interface 58 for insertion into a signaltelemetry format provided by a telemetry transceiver 60. The telemetrytransceiver 60 can transmit signals to the earth's surface correspondingto the calculated magnitudes. Alternatively, magnitude values calculatedin the controller 58 may be stored in an appropriate recording device(not shown) for processing after the instrument 10 is withdrawn from thewellbore (2 in FIG. 1).

The arrangement of transmitter coils and receiver coils on the coilmandrel unit 8 can be better understood by referring to FIGS. 3A and 3B.The transmitter coil section of the coil mandrel unit 8 is shown in FIG.3A. A transmitter coil which can be wound so that its axis, and therebyits magnetic moment, is along an axis X1 is shown at TX. Axis X1 byconvention will be referred to as being parallel to the X-axis. Coil TXis preferably substantially perpendicular to the axis of the instrument(10 in FIG. 1). Coil TX can be electrically connected to the output ofone of the power amplifiers (such as 16 in FIG. 2). When alternatingcurrent flows through transmitter coil TX, an alternatingelectromagnetic field is in induced, which causes eddy currents to flowin "ground loops" in the wellbore (2 in FIG. 1) and in the earthformation (4 in FIG. 1) substantially coaxially about axis X1 andparallel to the axis of the mandrel unit 8 and the instrument (10 inFIG. 1).

A short distance along the axis of the coil mandrel unit 8 can beanother transmitter coil TZ. Coil TZ can be wound so that it axis Z1 issubstantially parallel to the axis of the instrument 10 (which byconvention is generally referred to as the Z-axis). Coil TZ can beconnected to the output of another one of the power amplifiers (such as20 in FIG. 2). Alternating current passing through coil TZ induces eddycurrents in the wellbore 2 and formation 4 which flow in ground loopssubstantially coaxial with axis Z1 and substantially perpendicular tothe axis of the mandrel unit 8.

Located a short distance further along the axis of the mandrel unit 8can be a mutual balancing or "bucking" coil BX, corresponding to theX-axis transmitter coil TX. The winding axis X2, and therefore themagnetic moment, of coil BX can be substantially parallel to the axis X1of coil TX. Coil BX can be series connected in opposite polarity to coilTX, between coil TX and power amplifier 16. Bucking coil TX providesthat the output of a corresponding X-axis receiver coil (which will befurther explained) is substantially zero when the instrument is disposedin a non-conductive medium such as air. As is understood by thoseskilled in the art, using "bucking" coils to null the correspondingreceiver coil output in a non-conductive environment can be performedeither by providing such bucking coils connected in series with thecorresponding receiver coil, or alternatively can be connected in serieswith the transmitter coil. In the present embodiment of the invention itis preferable to provide a bucking coil in series with the correspondingtransmitter coil to simplify impedance matching between thecorresponding receiver coil and its associated preamplifier (such as 44in FIG. 2), and thereby to improve the ability of the circuitryassociated with each receiver coil to handle signals over a widefrequency range. The reactance of a bucking coil and its associatedwiring would complicate impedance matching, and adjusting for signalresponse characteristics for a wide band response receiver coil, whenconnected in series with the receiver coil because this reactance isfrequently nearly the same as the reactance of the receiver coil.

Still another short distance along the axis of the mandrel unit 8 is aY-axis transmitter coil TY. Coil TY is preferably wound so that its axisY1, and therefore its magnetic moment, are substantially perpendicularto both the axis of the instrument 10 and to the magnetic moment of coilTX. Coil TY can be connected to power amplifier 18. Alternating currentflowing through coil TY induces a magnetic field which causes eddycurrents to flow in the wellbore 2 and the earth formation 4 in groundloops substantially coaxial with axis Y1 and parallel to the axis of theinstrument 10. The eddy current ground loops corresponding to coil TYwould also be substantially perpendicular to the ground loops associatedwith coils TX and TZ if the coils TX, TY, TZ are arranged as describedherein.

Bucking coils associated with transmitter coils TZ and TY are shown atBZ and BY, respectively. Bucking coils BZ and BY are electricallyconnected between their respective transmitter coils TZ, TY and poweramplifiers 20, 18 in opposite polarity, as is bucking coil BX. Buckingcoil BZ is wound to have its axis and magnetic moment along Z2 and BY iswound to have its axis and magnetic moment along Y2. Z2 is substantiallyparallel to Z1, and Y2 is substantially parallel to Y1.

A suitable arrangement of receiver coils for the invention is shown inFIG. 3B. At the lowermost end of the receiver coil section of the coilmandrel unit 8 can be an X-axis receiver coil RX. Coil RX can be woundso that its sensitive direction is parallel to axis X1 as fortransmitter coil TX (shown in FIG. 3A). Eddy currents flowing in groundloops corresponding to coil TX will induce voltages in coil RXproportional in magnitude to the magnitude of the previously explainedTX-related eddy currents. The eddy currents themselves are proportionalto the electrical conductivity in the path of these ground loops.

A short distance along the axis of the coil mandrel unit 8 is a Z-axisreceiver coil RZ wound to have its sensitive direction substantiallyparallel to Z1, as for its corresponding transmitter TZ. Eddy currentsflowing in the previously explained ground loops related to coil TZ willinduce voltages in coil RZ proportional to the magnitude of these eddycurrents.

The mandrel unit 8 can include a Y-axis receiver coil having a sensitivedirection parallel to Y1 and is shown at RY. Eddy currents associatedwith coil TY will induce similar type voltages in coil RY.

If the layers of the earth formations (4A through 4F in FIG. 1) aresubstantially perpendicular to the axis of the mandrel unit 8, thenmeasurements made by the Z-axis coils in combination with measurementsmade by either the X- or Y-axis coils would be sufficient to resolveanisotropy of the conductivity of the earth formations. It is frequentlythe case, however, that the layers 4A-4F are not perpendicular to theaxis of the mandrel unit 8 either because the wellbore (2 in FIG. 1) isinclined from vertical, or the layers 4A-4F are not horizontal (referredto in the art as "dipping beds") or a combination of these two factors.Therefore in order to resolve the anisotropy of the conductivity, thecoil mandrel unit 8 of the invention preferably includes cross-axialreceiver coils. One such cross-axial receiver coil is shown at CXY. CoilCXY receives voltages induced as a result of eddy current magneticfields which are parallel to the Y1 axis (parallel to the magneticmoment of the Y-axis transmitter coil TY). These eddy currents may beinduced as a result of current flowing through transmitter coil TX. Aspreviously explained, coil TX includes bucking coil BX to null theoutput of receiver coil RX in a non-conductive environment. Since coilCXY is located at a different axial spacing than coil RX, however,nulling the output of coil CXY would require a bucking transmitter coillocated at a different axial position than coil BX. As a matter ofconvenience for the system designer, the output of coil CXY can benulled by including a receiver bucking coil connected in series andopposite polarity with coil CXY. This receiver bucking coil is shown atBXY. Methods of adjusting the axial position of receiver bucking coilssuch as BXY to null the output of the corresponding receiver coil CXYare well known in the art. The present embodiment of the inventionincludes cross-component coil CXY instead of merely using receiver coilRY for the same reason as coil CXY includes associated bucking coil BXY,namely that nulling the output of receiver coil RY to match transmittercoil TX in a non-conductive environment would require the use of anadditional bucking coil for cross component detection, as well as theoriginal bucking coil for direct detection of the signal from itsassociated transmitter coil (TY in this case). As a matter ofconvenience for the system designer the present embodiment includesseparate cross-component coils such as CXY. It is to be understood thatRY could be used for cross-component detection when combined with anappropriate bucking coil, and therefore the use of separatecross-component coils should not be construed as a limitation on theinvention.

Another cross-axial receiver coil which can be included in the inventionis shown at CXZ. Coil CXZ receives voltages induced along the Z-axiscaused by eddy currents flowing in the earth formation as a result ofcurrent flowing through the X-axis transmitter coil TX (along X1). CoilCXZ can include a receiver bucking coil BXZ similar in function tobucking coil BXY. Adjusting the combined output of coils BXZ and CXZ tobe zero in a non-conductive environment can be performed in a similarmanner to that used to null the combined output of coils CXY and BXY ina non-conductive environment.

The electrical connections between the receiver coils and thereceiver/signal processing/telemetry electronics unit (12 in FIG. 2) canbe better understood by referring once again to FIG. 2. Receiver coil RXcan be connected to the input of preamplifier 32. Receivers RY and RZare connected, respectively, to the inputs of preamplifiers 34 and 36.Cross-axial receiver coil CXY and bucking coil BXY are series connectedto the input of preamplifier 38. Cross-axial receiver coil CXZ andbucking coil BXZ are series connected to the input of preamplifier 40.Preamplifiers 32-40 are each selected to provide a signal output levelcompatible with the dynamic range of analog to digital converter portionof the ADC/DSP circuit connected the output of each preamplifier. Aspreviously explained, each preamplifier 32, 34, 36, 38, 40 can beconnected to an associated ADC/DSP 54, 52, 50, 48, 46.

The ADC/DSP's 54, 52, 50, 48, 46 each generate digital samples of theoutput of the preamplifier connected to it. The acquisition of thedigital samples is timed by the controller 56. The controller 56 can beprogrammed to cause each associated ADC/DSP to generate digital samplesof the output of the corresponding preamplifier. The controller 56commands each ADC/DSP to generate a plurality of samples during eachcycle of the alternating current flowing through each of the transmittercoils. These digital signal samples can be timed to have a predeterminedphase with respect to the alternating voltages induced in each of thereceiver coils RX, RY, RZ, CXY, CXZ. The significance of the timing ofthe digitization will be further explained.

The hardware configuration of the instrument 10 having been explained,the timing and control of the power amplifiers (16, 18, 20 in FIG. 2)and the ADC/DSP's (54, 52, 50, 48, 46 in FIG. 2) will be explained inmore detail. Referring now to FIG. 4, the transmitter controller 24 caninclude a read only memory (ROM) 62 which contains a digitalrepresentation of the desired waveform of the current to be passedthrough transmitter coils (TX, TY, TZ in FIG. 3A). The digitalrepresentation typically consists of numbers corresponding to themagnitude of the desired waveform sampled at spaced apart timeintervals. The output of the ROM 62 is timed by a clock 64, which mayform part of the transmitter controller 24, so that the numbers exit theROM 62 at spaced apart time intervals and are conducted to a digital toanalog converter (DAC) 66. The DAC 66 converts the numbers conductedsequentially from the ROM 62 into corresponding fractional amounts of areference voltage source [V_(ref) ] 70 connected to the DAC 66. Theoutput of the DAC 66 then consists of analog voltages proportional tothe numbers input from the ROM 62. Since the output of the DAC 66changes in step with each new number conducted from the ROM 62, the DAC66 would appear if graphed as a series of "stair-steps" The output ofthe DAC 66 is therefore preferably conducted to a low-pass filter 68 tosmooth the "stair-step" like output of the DAC 66 into a continuous,smooth waveform. The output of the filter 68 can be conducted to theinput of each power amplifier (16, 18, 20 in FIG. 2). It is to beunderstood that using the digital circuit just described herein forgenerating a driver signal for the power amplifiers 16, 18, 20 is amatter of convenience for the system designer and is meant only to serveas an example of circuits which could generate the desired transmittercurrent waveform. Analog signal generator circuits could as easilyperform the required signal generation function.

As previously explained, a reference tap on each power amplifier 16, 18,20 conducts a portion of the transmitter current to the ADC/DSP 26 inthe auxiliary electronics unit 14. The ADC/DSP 26 generates digitalsamples of the transmitter current and conducts the samples to thetransmitter controller 28. The transmitter controller 28 can calculatedifferences between the digitized samples of the transmitter current andthe numbers stored in the ROM 62. These differences can include changesin amplitude and phase of the transmitter current with respect to thedesired amplitude and phase of the transmitter current. Thesedifferences can be used to generate adjustment factors for the numbersstored in the ROM 62 so that the desired amplitude and phase can be moreclosely generated in the transmitter current. It is to be understoodthat analog circuitry known in the art can be used to perform theadjustments to the transmitter current waveform as just described. Theuse of the digital circuitry described herein for adjusting thetransmitter current waveform is a matter of convenience for the systemdesigner and is not meant to limit the invention. The changes calculatedbetween the numbers in the ROM 62 and the digitized transmitter currentcan also include a number of cycles of the clock 64, whereby can bedetermined the actual phase of the transmitter current with respect tothe apparent phase of the transmitter current waveform as synthesized bythe numbers output from the ROM 62. It is contemplated that the clock 64can have a sufficiently high frequency whereby this phase difference canbe determined to a very high degree of precision. The number of clockcycles of phase difference can be conducted to the controller (56 inFIG. 2) in the telemetry unit (12 in FIG. 2) over a serial link, shownin FIG. 2 as 30B. The clock 64 can be used to operate both thetransmitter controller 28 and the controller (56 in FIG. 2) so thatgeneration of digital signal samples of the receiver voltages can bemore accurately synchronized to the transmitter current.

A method of signal processing known as "frequency focusing" enablesdetermination of the conductivity of the earth formations, particularlyin directions along the X- and Y-axes, while substantially excluding theeffects of eddy currents flowing in the wellbore (2 in FIG. 1). In anovel aspect of the invention, frequency focusing can be performed byhaving the transmitter current waveform include sinusoids at twodifferent frequencies, combined in a predetermined relationship ofamplitude and phase between each component frequency. The frequency forthe transmitter current can be within a range of about 10-70 KHz for thefirst frequency and about 30-210 KHz for the second frequency, as willbe further explained.

In the present embodiment of the invention, the transmitter currentwaveform, represented by I_(T), should follow the relationship:

    I.sub.T =I.sub.T1 +I.sub.T2                                (1)

where I_(T1) and I_(T2) represent, respectively, the transmitter currentwaveforms at the first ω₁, and the second ω₂ component frequencies, andwhere the relative amplitudes of I_(T1) and I_(T2) follow therelationship: ##EQU1## where I₀ represents an arbitrary referencemagnitude, typically proportional to the level of V_(ref) (70 in FIG.4). It is desirable for ω₂ to be an odd-number harmonic multiple of ω₁,and in the preferred embodiment, ω₂ is the third harmonic. Thetransmitter current waveforms at the two component frequencies shouldhave the same initial phase (zero) at the beginning of each cycle of thetransmitter current at the first frequency. It has been determined thatif the transmitter current follows the magnitude relationship describedin equation (2), then the desired signal characteristics of the voltagesinduced in the receiver coils (RX, RY, RZ, CXY, CXZ in FIG. 3B) can bedetermined by directly measuring components of the induced voltageswhich have a certain time relationship with respect to the currentflowing through the transmitter coils (TX, TY, TZ in FIG. 3A) at thefirst frequency. The components, at these times, of the voltages inducedin the receiver coils by a two-frequency magnetic field having thefrequency, phase and amplitude relationship described in equations , and2 are inherently substantially insensitive to voltages induced by eddycurrents flowing in the wellbore (2 in FIG. 1) and are substantiallycorrespondent only to the magnitude of the eddy currents flowing only inthe earth formations. By selecting the two component frequencies andrelative amplitudes for the transmitter current waveform as described inequation (2), the conductivity of the earth formation can be directlyrelated to the difference between the components of the induced voltagesat each component frequency.

In this embodiment of the invention, the difference in the magnitudes ofthe components of the induced voltages at the two frequencies can bemeasured directly by programming the controller (56 in FIG. 2) to timeacquisition of digital signal samples, represented by t_(n), to occurtwice during each full cycle of the transmitter voltage at the first(lower) frequency according to the expression: ##EQU2## The digitalsamples of the induced voltages in the receiver coils made at thesetimes will directly represent the difference in magnitude between thecomponents of the induced voltage at each frequency. The digital signalsamples made at these times can then be directly related to theconductivity of the earth formations.

The manner in which the magnitude of these digital signal samplesdirectly represents the difference between the induced voltagemagnitudes at the first and second component frequencies can be betterunderstood by referring to FIGS. 5A, 5B, 6A and 6B. FIG. 5A shows agraph of each of the two frequency components of the alternating currentflowing through the transmitter coil. The current magnitude at the firstfrequency is represented by curve I_(T1), and the current magnitude atthe second frequency is shown by curve I_(T2). As previously explained,the second frequency can be the third harmonic multiple of the firstfrequency and have an amplitude relationship as previously described inequation (1). The composite current waveform is shown in FIG. 5B asI_(T). The voltage which is induced in the receiver coil as a result ofeddy currents flowing in the formation is shown in FIG. 6A, wherein theeddy currents are induced by the magnetic field generated by the current(I_(T) in FIG. 5B) flowing through the transmitter coil. Digital signalsamples can be made at times shown in FIG. 6A. Sample 1 is shown astimed to be at one-quarter cycle at the first frequency (1/2π/ω₁). Thistime corresponds to n=0 in equation (3). Sample 2 is shown timed atthree-quarter of the cycle at the first frequency (3/2π/ω₁), whichcorresponds to n=1 in equation (3). The reason that digital samples madeat these relative times represent the difference in magnitudes betweenthe receiver voltage components at the first and at the secondfrequencies can be better understood by referring to FIG. 6B, whichshows the receiver voltage as its individual frequency components: atthe first frequency, shown by curve V_(R) @ ω_(l) ; and at the secondfrequency, shown by curve V_(R) @ ω₂. If the alternating current wereapplied at each frequency individually to the transmitter coil, thevoltage induced in the receiver coil would be shown by the individualcomponent curves as in FIG. 6B. If the current at the second frequencyhas the frequency and timing relationship with respect to the current atthe first frequency, as described herein, the induced voltage at thefirst frequency will reach a peak value at the times at which theinduced voltage at the second frequency will reach a peak value but atthe opposite polarity. Since the two frequencies of current aresuperimposed (passed through the transmitter simultaneously), samples ofthe voltage induced in the receiver coil taken at the times shown inFIG. 6B, such as SAMPLE 1 and SAMPLE 2, will therefore directlyrepresent the difference between the peak magnitudes of the inducedvoltage components at the first and at the second frequency.

Referring once again to FIG. 2, when the instrument 10 is firstenergized, the transmitter controller 24 begins to generate a full cycleof the transmitter voltage waveform. The output of the transmittercontroller 24, as previously explained, is conducted to the timercontroller 22. In the preferred embodiment of the invention, X-, Y, andZ-axis measurements can be conducted sequentially. The transmittercontroller 24 can send a command signal to the timer controller 22 tocause it to actuate the particular power amplifier (such as X-axisamplifier 16) whose transmitter coil connected thereto corresponds tothe axis along which the particular measurement is to be made. It iscontemplated that a sufficiently precise measurement can be made byoperating the transmitter controller through about 1,000 transmittervoltage waveform cycles at the first (lower) frequency, although thisnumber of cycles is not to be construed as a limitation on theinvention. For example, if the instrument 10 is to be moved relativelyslowly through the wellbore (2 in FIG. 1), then a larger number ofcycles may be useable in order to obtain higher accuracy measurements.

After the transmitter controller has operated through about 1,000cycles, the transmitter controller 28 can instruct the timer controller22 to operate another one of the amplifiers, such as Y-axis amplifier18, to conduct the alternating current to its associated transmittercoil (TY in FIG. 3A). After about another 1,000 cycles, the transmittercontroller 28 can instruct the timer controller to repeat the processfor the remaining (Z-axis) power amplifier 20, and after about 1,000cycles of alternating current have passed through the Z-axis transmittercoil (TZ in FIG. 3A), the entire process can be repeated.

During transmission from a particular transmitter coil, the controller56 sends command signals to the ADC/DSP's 46-54 which are connected tothe receiver coils which are to be detected during operation of eachparticular transmitter coil. For example, during operation of X-axistransmitter coil TX, ADC/DSP's 54 (connected to preamplifier 32, whichis connected to X-axis receiver coil RX) and 48 (connected topreamplifier 38, which is connected to cross-component receiver coilCXY) and 46 (connected to preamplifier 40, which is connected tocross-component receiver coil CXZ) are instructed to digitize the outputof the associated preamplifiers. The controller 56 can instruct thecorresponding ADC/DSP's to generate digital signals samples at the exacttimes described in equation (3) with respect to the transmitter voltage.Alternatively, the ADC/DSP's can generate at least four samples for eachcycle at the second (higher) frequency. Since the controller 56 and thetransmitter controller 24 can be timed by the same clock (64 in FIG. 4),the exact time of generating the digital signal samples must be adjustedby the phase delay determined as previously described in the transmittercontroller 24. The controller 56 can delay sending instruction todigitize the preamplifier output by the number of clock cycles of phasedelay conducted from the transmitter controller 24 with respect to astart of transmitter voltage cycle command. The start of transmit cyclecommand can also be sent along the serial link 30B to indicate to thecontroller 56 that the transmitter controller 24 is initiating atransmitter voltage cycle. The digital signal samples acquired duringthe transmitter voltage cycle can be synchronously stacked, aspreviously described herein, and can be stored in a buffer (not shownseparately) in the controller 56 for transmission to the surface by thetelemetry transceiver 60, or can be retained for later processing. Aspreviously described, the samples from each ADC/DSP 54-46 can beprocessed by a discrete Fourier transform to determine the magnitude ofthe voltage components at each frequency, or the samples made at theprecise times described in equation (3) can be used to determine thedifference in the in-phase voltage components directly.

After the previously described number of transmitter voltage cycles(which as previously explained can be about 1,000), the controller 56can send digitization commands to the ADC/DSP associated with thereceiver coil which will receive voltages induced by its axiallyassociated transmitter coil (such as ADC/DSP 52 associated with coils RYand TY). The receiving and digitization process can then be repeated forthe remaining transmitter coil and axially associated receiver coil.

2. Processing transverse induction signals into an estimate of the axialpositions of formation layer boundaries

The first step in the method of the invention is to calculate a secondderivative, with respect to axial position (wellbore depth), for thereceiver signals measured by either the X-axis (RX in FIG. 3A) or theY-axis (RY in FIG. 3A) receiver coils. The receiver signal should be theone measured from the magnetic field generated by the transmitter coiloriented along the same axis as the receiver coil. If the signal fromthe RX receiver coil is used, it should correspond to alternatingcurrent passed through the X-axis transmitter coil (TX in FIG. 3A).Similarly, if the signal from the RY receiver coil is used, it shouldcorrespond to the alternating current being passed through the Y-axistransmitter coil (TY in FIG. 3A). Such receiver signals are generallytransverse to the axis of the instrument and are parallel to theboundaries of the earth formation layers. These signals can be generallycharacterized as "transverse" induction signals.

In the invention, the receiver signal used for calculating the secondderivative should be measured using only a single frequency alternatingcurrent passing through the corresponding transmitter coil, rather thanthe special two-frequency alternating current described earlier herein.As will be further explained, the method of the invention can berepeated for transverse induction measurements made at a plurality ofdifferent individual alternating current frequencies to enhance thereliability of the results.

An example of the response of the RX receiver coil to the magnetic fieldgenerated by the TX transmitter at an alternating current frequency of20 KHz is shown in FIG. 7. FIG. 7 represents a synthesized response ofthe RX receiver coil to a simulated earth formation having five, 3 meterthick anisotropic layers embedded in an isotropic surrounding earthformation. The axial positions of the anisotropic layers are indicatedon the depth scale on the left-hand side of the graph in FIG. 7. Thelayers are generally transverse to the axis of the instrument. Thesynthetic signals were corrupted with Gaussian distributed random noisehaving a standard deviation of about 0.66 μA/m. The relative amplitudeof the noise with respect to the signal amplitude increases with respectto the depth within the modeled earth formations.

The second derivative of the RX receiver coil response is shown over thesame modeled earth formations in FIG. 8. The second derivative withrespect to depth can be stored in a depth-referenced file similar inform to the depth-referenced files in which the "unprocessed" receivervoltage signals are recorded for processing. Such file formats are wellknown in the art.

The next step in the method of the invention is to "mute" the secondderivative values to reduce the effects of noise and enhance thereliability of the results. An example of muting is shown in FIG. 9.Values of the second derivative which exceed a selected threshold areretained, while all values of the second derivative which fall below thethreshold are set to zero.

Then a first derivative with respect to depth can be calculated from thesame receiver signals used to calculate the second derivative. The firstderivative values are scanned with respect to depth. At each axial(depth) position where the first derivative changes sign (passes throughzero), the value of the second derivative is examined. If the value ofthe second derivative is non-zero at any position where the firstderivative changes sign, a bed boundary is inferred. The inferred bedboundary can be written as a non-zero value indication to adepth-referenced file.

Locations of bed boundaries inferred from the first and secondderivatives can then be filtered to eliminate locations unlikely to havea bed boundary. This procedure can be referred to as "thickness"filtering. A minimum thickness threshold related to the axial spacingbetween the transmitter and receiver coil can be selected. The receivervoltage measurements used in this invention have a minimum axialresolution which is related to the axial spacing between the transmitterand receiver coils used to make the measurements. Layer boundaryindications which occur at axial positions separated from the previouslayer boundary indication, by less than the minimum thickness threshold,can be removed from the layer boundary indication file.

After the minimum thickness filter is applied, it is desirable to filterout any layer boundary indications having axial separations from theprevious layer boundary indications of 0.6 and 1.6 meters, when usingthe instrument coil arrangement shown in FIGS. 3A and 3B. The values of0.6 and 1.6 meters represent the spacing between the transmitter coil(TX in FIG. 3A) and main receiver coil (RX in FIG. 3A), and the spacingbetween the transmitter coil TX and the bucking coil (BX in FIG. 3B).The spacing values used for this filtering step will depend on theactual spacing between the transmitter and receiver coils whose signalsare used for layer boundary detection, so the 0.6 and 1.6 meter spacingsare not meant to strictly limit the invention. An example of the layerboundary response after the steps of thickness filtering is shown inFIG. 10.

To further improve the results of the method, the entire procedure canbe repeated using single-frequency receiver voltage signals, from thesame receiver coil (based on the magnetic field generated by the sametransmitter coil), but made at a different alternating currentfrequency. The instrument disclosed herein includes the capability tomake induction voltage measurements at a plurality of individual andcombined frequencies within a range from about 10 to 210 KHz. Layerboundaries inferred from the thickness-filtered first and secondderivatives, made at each individual frequency, can be compared to thelayer boundary inferences from the measurements at each other frequency.Layer boundary inferences appearing in the calculations made fromsignals measured at more than one different frequency can be selected asthe locations of layer boundaries for further processing such as byinversion.

DESCRIPTION OF AN ALTERNATIVE EMBODIMENT

An alternative embodiment of the invention includes calculation of afirst derivative of the transverse induction receiver measurements inthe spatial frequency domain. The transverse induction measurements canbe made from the same transmitter and receiver coils as for the firstembodiment of the invention. Similarly as for the first embodiment ofthe invention, the transverse induction measurements are preferably madeat a single alternating current frequency. This is shown in FIG. 11 inbox 100. The first step in this embodiment of the invention is toconvert the transverse induction measurements with respect to depth intothe spatial frequency domain by using a Fourier transform. The term"spatial frequency" is stated here to avoid confusion with the frequencyof the alternating current used to make the induction measurements. Theoutput of the Fourier transform will include relative amplitude andphase of the induction signals with respect to spatial frequency. TheFourier transform is shown in box 102 in FIG. 11.

The Fourier transformed transverse induction measurements should then befiltered using a low pass filter with a band limit corresponding to theaxial resolution of the logging instrument. As explained in the previousembodiment of the invention, the axial resolution will be related to theaxial spacing between the transmitter and receiver coil used to make theinduction measurements. The low pass filter should include a taper atthe band limit to reduce the magnitude of artifacts in the processedresults known as Gibb's ringing. The step of low pass filtering is shownin box 104 in FIG. 11.

The next step in this embodiment of the invention is to calculate acentral derivative of the filtered, Fourier transformed signals. Thisstep can be described as follows. The induction signals are recorded asa series of discrete values with respect to depth, with the depthinterval generally being equal between each recorded depth. The Fouriertransform will typically be a discrete Fourier transform. Therefore thecoordinates in the Fourier transform will be represented by discreteindividual frequency values. Calculating a central derivative includescalculating a value of induction voltage which would obtain at aboutone-half depth level above, and one-half depth level below each recordeddepth level in the recorded voltage signals. The value of inductionvoltage which would obtain at one-half depth level either above or beloweach recorded depth level can be calculated by applying an appropriatephase shift to the Fourier spectrum. Then, the Fourier transform of thedifference between the one-half depth level shifted values, and thevalues of induction voltage which would obtain one full depth levelabove or below each of the one-half depth level shifted values can becalculated using a formula shown for example in, H. Joseph Weaver,"Applications of Discrete and Continuous Fourier Analysis", John Wileyand Sons, New York (1983) p. 91-96. Then the inverseFourier-transforming of the difference spectrum is calculated. Theinverse Fourier transform of the difference spectrum results in thecentral difference approximation of the numerical derivative of thevoltage signals at each recorded point in the depth (space) domain. Thecalculation of the central derivative is shown in FIG. 11 in box 106.The result is an approximation of the first derivative of the originalinduction measurements filtered to remove any layer boundary indicationsat an axial spacing less than the axial resolution of the instrument.The step of inverse Fourier transforming is shown in box 108 in FIG. 11.

Formation layer boundaries can be inferred at each location where thefirst derivative passes through a value of zero (the "roots" of thederivative). The roots of the derivative will typically indicate all thelayers in the formation, but may include layer indications which do notcorrespond to a true layer boundary. To verify the nature of layerboundary indications as representing a true layer boundary, localizedproperties of the derivative can be tested. Localized properties refersto changes in the value of the induction measurements or the derivativewithin a few depth levels of the depth level of interest. Theselocalized properties can include peak widths, the integral surface underthe peak, and the axial range of consistent (directionwise) change inthe value of the first derivative. For example, all peaks or troughsnarrower than four contiguous depth level points can be discarded as notbeing representative of a true layer boundary. Similarly, change invalue of the first derivative which does not continue in the samedirection (increasing or decreasing in value) of less than about fourdata points can be discarded. Testing the localized properties is shownin box 110 in FIG. 11.

The system operator may wish to test the results by recalculating theaxial positions of layer boundaries using single alternating currentfrequency measurements made at each of the other different alternatingcurrent frequencies, just as for the first embodiment of the invention.This is shown in decision box 112 in FIG. 11. It should be noted thatthis embodiment of the invention typically does not miss any layerboundaries at any individual alternating current (AC) frequency, so thestep of repeating the process at different AC frequencies should beconsidered optional.

Those skilled in the art will devise other embodiments of the inventionwhich do not depart from the spirit of the invention as disclosedherein. Accordingly, the invention should be limited in scope only bythe attached claims.

What is claimed is:
 1. A method for estimating axial positions offormation layer boundaries from transverse electromagnetic inductionsignals measured at a selected frequency, comprising:calculating a firstderivative with respect to depth of said transverse induction signals;calculating a second derivative with respect to depth of said transverseinduction signals; muting said second derivative; selecting layerboundaries at axial positions where said muted second derivative is notequal to zero and where said first derivative changes sign; thicknessfiltering said selected layer boundaries.
 2. The method as defined inclaim 1 further comprising repeating said steps of calculating saidfirst and said second derivatives, muting, selecting and filtering, fortransverse induction measurements made at a different alternatingcurrent frequency than said selected frequency, and selecting locationsof layer boundaries where said thickness filtered selected layerboundaries occur at the same axial position for both said frequencies.3. The method as defined in claim 1 wherein said step of thicknessfiltering comprises eliminating ones of said selected boundaries havingan axial spacing equal to a spacing between an induction transmitter andan induction receiver used to measure said transverse induction signals.4. The method as defined in claim 1 wherein said step of thicknessfiltering comprises eliminating ones of said selected boundaries havingan axial spacing less than an axial resolution of said transverseelectromagnetic induction signals.
 5. A method for estimating axialpositions of formation layer boundaries from transverse electromagneticinduction signals measured at a selected frequency, comprising:Fouriertransforming said signals into the spatial frequency domain; low passfiltering said Fourier transformed signals at a cutoff about equal to anaxial resolution of said induction signals; calculating a central firstderivative of said filtered Fourier transformed signals; calculating aninverse Fourier transform of said central first derivative; selectingroots of said inverse Fourier transformed central first derivative; andtesting localized properties of said inverse Fourier transformed centralfirst derivative within a selected number of data sample points of saidroots, thereby providing indications of formation layer boundaries ataxial positions most likely to be true ones of said formation layerboundaries.
 6. The method as defined in claim 5 further comprisingrepeating said steps of Fourier transforming, low pass filtering,calculating said central derivative, inverse Fourier transforming,selecting said roots and testing said localized properties fortransverse electromagnetic induction signals measured at a differentfrequency than said selected frequency.